Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Improving Efficiency of the Moment Estimator of the Extreme Value Index

  • Yun, Seokhoon (Department of Applied Statistics, University of Suwon)
  • Published : 2001.09.01
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Abstract

In this paper we introduce a method of improving efficiency of the moment estimator of Dekkers, Einmahl and de Haan(1989) for the extreme value index $\beta$. a new estimator of $\beta$ is proposed by adding the third moment ot the original moment estimator which is composed of the first two moments of the log-transformed sample data. We establish asymptotic normality of the new estimator and examine and adaptive procedure for the new estimator. The resulting adaptive estimator proves to be asymptotically better than the moment estimator particularly for $\beta$<0.

Keywords

References

  1. Statistical Extremes and Applications Slow variation and characterization of domains of attraction de Haan, L;J. Tiago de Oliveira(ed)
  2. Ann. Statist. v.17 On the estimation of the extreme-value index and large quantile estimation Dekkers, A.L.M;de Haan, L
  3. Ann. Statist. v.17 A moment estimator for the index of an extreme-value distribution Dekkers, A.L.M;Einmahl, J.H.J;de Haan, L
  4. Ann. Statist. v.23 Refined Pickands estimators of the extreme value index Drees, H
  5. Ann. Statist. v.13 On asymptotic normality of Hill's estimator for the exponent of regular variation Haeusler, E;Teugels, J.L
  6. Ann. Statist. v.3 A simple general approach to inference about the tail of a distribution Hill, B.M
  7. Ann. Probab. v.10 Laws of large numbers for sums of extreme values Mason, D.M
  8. Extreme Value Theory and Applications III Second order behavior of domains of attraction and the bias of generalized Pickands' estimator Pereira, T.T;J. Galambos(ed);J. Lechner(ed);E. Simiu(eds)
  9. Ann. Statist. v.3 Statistical inference using extreme order statistics Pickands, J
  10. Approximation Theorems of Mathematical Statistics Serfling, R.J
  11. J. Statist. Plann. Inference v.83 A class of Pickands-type estimators for the extreme value index Yun, S